Turkish Journal of Mathematics
Abstract
Let $ A_\varepsilon (x,f)$ be the Abel-Poisson means of an integrable function $f(x)$ on $n$-dimensional torus $ \mathbf{T}^n, \; \;\; i= 1,\ldots,n \; (n\geq 2) $ in the Euclidean $n$-space. The famous Bochner's theorem asserts that for any function $ f\in L^1(\mathbf{T}^n)$ the Abel-Poisson means $A_\varepsilon (x,f)$ are pointwise converge to $f(x)$ a.e., that is, $$ \underset{\varepsilon \rightarrow0^+}{\lim}\, A_\varepsilon (x,f)= f(x), \;\; a.e.\; x\in \mathbf{T}^n. $$ In this paper we investigate the rate of convergence of Abel-Poisson means at the so-called $\mu$-smoothness point of $f$ .
DOI
10.55730/1300-0098.3160
Keywords
Abel-Poisson means, multiple Fourier series, Poisson summation formula
First Page
1302
Last Page
1309
Recommended Citation
SEZER, S, ERYİĞİT, M, & BAYRAKÇI, S (2022). On the convergence of the Abel-Poisson means of multiple Fourier series. Turkish Journal of Mathematics 46 (4): 1302-1309. https://doi.org/10.55730/1300-0098.3160
